Good discussion, so far. I know everyone has different ideas on athleticism, but let me clarify my original question.
First, when I said what sport produces the best athlete, that's exactly what I meant. Meaning, forget about genetics or muscle composition... assume all other factors are equal. Think about the specific training each sport emphasizes, and what the athlete gains from this training. For instance, the average training of a marathon runer will not emphasize upper-body strength like the training of a basketball player.
Second, I'm assuming the representative athlete is from the highest level of that sport, be it college, the Olympics, or professional.
Third, here's my definition of "best athlete", at least for this context. The best athlete is the one who, if placed in a number of physical contests of varying requirements, would finish the highest in the largest number of those contests. Contests could be long-distance running, lifting heavy objects, having the quickest reaction time, shooting an arrow, whatever. In short, I'm saying the most physically balanced athlete, who can rapidly adapt to any situation, is the best athlete. That's why my pick was an amateur wrestler, since the training of that sport covers just about every physical attribute you can imagine.